“Black-on-black crime.”
White people, banish this phrase from your mind. Wash it out of your mouth. If you type it without scare quotes, cut off your fingers and cast them from you, for it is better for you to lose your fingers than for your whole body to be thrown into hell.
Let us state the social issue before us: Black men are being killed by police and vigilantes because they are presumed to be criminals. They can follow police instructions and still be killed, like Philando Castile. They can be killed for playing in a park, like Tamir Rice. They can be killed for wearing a hoodie and buying skittles, like Trayvon Martin. They can be killed for exercising their second-amendment rights, like EJ Bradford. In all of these cases, the victims were presumed to be criminals by those doing the shooting.
They can be killed without consequence because the assumption is that black men are dangerous. Did the police officer / vigilante fear for their life? Of course they did: the victim was a black man, and everyone of us has been programmed to believe that black men are dangerous.
So when a black man is killed (again), and people protest his killing, some white folks (and a few black folks) respond with this dismissive, distracting rhetoric which reinforces the stereotype: “What about black-on-black crime?” “Why don’t you protest that?”
The genius of this evil turn of phrase is that it allows someone to sound concerned while they reassert one of the central premises of white supremacy: black people are defective. In some ontological, primordial way, their blackness is a signifier of their wickedness. They are prone to criminality. They are violent. So we need to address “black-on-black crime” before we can take seriously the idea that our black siblings are being killed without cause. According to this logic, ANY GIVEN KILLING of an unarmed or innocent black man is justified. Just like lynchings, modern vigilante justice will never be uncalled-for. Using the phrase “black-on-black crime” is a way of saying, “Black people brought this on themselves.”
There are, of course, many other reasons this phrase is nonsensical. As others have pointed out, we do not refer to mass shootings, anti-semitic hate crimes, or white-collar insider trading as “white-on-white” crime.

An anti-semitic riot in 1819, an example of “white-on-white” crime. https://en.wikipedia.org/wiki/Hep-Hep_riots
But the phrase “black-on-black crime” is abhorrent because it is intentionally used to dismiss white supremacist violence against black bodies. It obscures the violence while it justifies bullets fired, blood lost, parents bereaved, and children orphaned. It is a euphemism, a slightly-more polite way of using the N-word.
Take those words out of your mouth. Throw them away. Never, ever, ever use them again.